EXPERIMENTAL VERIFICATION OF THE LIMITING EQUATION FOR AN IRREVERSIBLE ANODIC PEAK AT A MERCURY FILM ELECTRODE

A. G. Stromberg, L. N. Popova

(Presented by the Scientific-Methodological Seminar of the Department of Chemical Technology)

In a previous work [1] we attempted to apply the limiting equation for an irreversible anodic peak at a mercury film electrode [2] to determine the composition of ammonia complexes of zinc that take a direct part in the process of anodic dissolution of zinc from zinc amalgam. In that work it was established that, under the conditions customary for the method of amalgam polarography with accumulation (APA), the results of calculations of the complex composition and of the transfer coefficient agree insufficiently well with the results of other investigators [3–8], who determined the kinetic parameters for this electrode process by other methods.

The aim of the present work is to study the influence of the rate of change of potential and of the thickness of the mercury film, over a sufficiently wide range of variation of these factors, on the peak potential of the anodic peaks of zinc at several concentrations of ammonia (ligand) in the solution, for a more detailed verification of the limiting equation for the anodic peak.

The work was carried out in a cell of conventional design [9], using an OH-101 polarograph (Hungary). The solution had the following composition: \(2 \cdot 10^{-5}\) g-ion/l Zn \((2+) + xMNH_3 + xMNH_4Cl + (3-x)MNaCl\). The ionic strength of the solution in all experiments remained constant and equal to 3. The experimental conditions were as follows: electrolysis potential, \(-1.5\) V; electrolysis duration, 2 min; solution volume, 3 ml. To maintain a constant concentration of ammonia in the solution, the nitrogen (used to remove oxygen from the air in the solution) was saturated with ammonia before the electrolyzer by passing it through several Drechsel bottles containing ammonia solution.

Special attention in the work was given to accurate measurement of the potentials of the anodic-peak maxima. The ohmic voltage drop in the cell did not exceed 0.001 V, and therefore it could be neglected. To reduce the inertia of the recorder, the work was carried out with zero damping of the recorder. Under these conditions the inertia of the recorder does not distort the current–voltage curves, as shown by experiments in recording an ordinary cathodic polarogram at a dropping mercury electrode in the forward and reverse directions. The half-wave potentials in both cases coincided with one another, which indicates the absence of any influence of the recorder inertia. All potential values in the text and in the figures are given relative to the saturated calomel electrode. The mercury film electrode was a silver wire 4 mm long and 1 mm in diameter (surface area \(0.13 \text{ cm}^2\)).

A mercury film of different thicknesses was obtained on this silver wire by carrying out electrolysis of a mercurous nitrate solution. The thickness of the mercury film in different experiments was varied from 1 to 30 $\mu$. The rate of change of potential was varied on an OH-101 polarograph within the range 100–1000 mV/min.

The limiting equation for the peak potential ($\varphi_{\mathrm{p}}$) of the anodic wave at a film electrode has the form [2]

\[ \varphi_{\mathrm{p}}=\varphi_{\mathrm{r}}-\frac{b}{\beta}\lg\frac{i_0RT}{z^2F^2Vc_2W\beta}, \tag{1} \]

where $\varphi_{\mathrm{r}}$ is the equilibrium potential, volts; $i_0$ is the exchange current, A; $\beta$ is the transfer coefficient; $V$ is the volume of mercury (amalgam) in the film, cm$^3$; $W$ is the rate of change of potential, V/sec; $c_2$ is the concentration of metal atoms (zinc) in the amalgam film, g-atom/cm$^3$; $b=2.3RT/zF=0.059/z$ (at 25°C); $z$ is the number of electrons participating in the electrode process per atom.

Let us express $i_0$, $\varphi_{\mathrm{r}}$, and $V$ in terms of other quantities:

\[ i_0=Sj_0c_3^{q_2-\beta p}c_1^\beta c_2^\alpha, \tag{2} \]

\[ \varphi_{\mathrm{r}}=\varphi_0+b\lg\frac{c_1}{c_2c_3^{q_2}}, \tag{3} \]

\[ V=S\cdot d, \tag{4} \]

where $S$ is the surface area of the film electrode, cm$^2$; $c_1$ is the concentration of (complex) metal ions in solution, g-ion/cm$^3$; $c_3$ is the ligand concentration, mole/cm$^3$; $p$ is the composition of the predominant equilibrium complexes in solution; $q_2$ is the composition of the complexes participating in the process of anodic dissolution of the metal from the amalgam; $j_0$ is the standard exchange-current density; $\varphi_0$ is the standard (formal) electrode potential; $d$ is the thickness of the mercury (amalgam) film, cm.

Substituting expressions (2)–(4) into (1), we obtain:

\[ \varphi_{\mathrm{p}}=\varphi_0-\frac{b}{\beta} \left[ \lg\frac{j_0RT}{z^2F^2\beta} -\lg d-\lg W+q_2\lg c_3 \right]. \tag{5} \]

It follows from expression (5) that under limiting conditions (very thin films and very low rates of change of potential), when diffusion is not the rate-limiting stage in the electrode process, the peak potential of the anodic wave must depend in the following manner on the factors of interest to us. In the coordinates $\varphi_{\mathrm{p}}, \lg d$ or $\varphi_{\mathrm{p}}, \lg W$, the plot, according to equation (5), must be represented by a straight line with slope $b/\beta=0.030/\beta$.

These straight lines, obtained at two different ligand concentrations ($c_3''$ and $c_3'$), must be parallel to one another on the indicated plots and separated by a distance $q_2 b/\beta\lg c_3''/c_3'$.

The dependence of the peak potentials on the rate of change of potential at small values of $W$ (from 0.1 V/min to 1 V/min) is presented in Fig. 1. It is seen that this dependence in the given interval of variation of $W$ is linear; the slopes of the straight lines are approximately identical and equal to $b/\beta=0.085$, which corresponds to $\beta=0.34$. This value of $\beta$ agrees with the data of works [5, 8], in which the coefficient $\beta$ in ammoniacal zinc solutions was determined by other methods. At higher rates of change of potential ($W>1$ V/min), the linear character of the dependence is disturbed (Fig. 2). In the mechanism

Fig. 1. Dependence of the peak potential of the anodic zinc wave on the rate of potential change (V/min) at different concentrations of ammonia (ligand) in solution. Curves: 1—0.10; 2—0.23; 3—0.86 mol/L \(NH_3\). Solution composition: \(2 \cdot 10^{-5}\) g-ion/L \(Zn^{2+} + xMNH_3 + xMNH_4Cl + (3-x)MNaCl\). Experimental conditions: pre-electrolysis potential \(\varphi_e = -1.5\) V; electrolysis time \(\tau = 2\) min; film thickness \(d = 5\,\mu\).

Fig. 2. Dependence of the potentials of the anodic zinc peaks on the logarithm of the rate of potential change (\([W]\)—V/min) at different concentrations of ammonia in solution: 1—0.13 mol/L; 2—0.4 mol/L; 3—2.5 mol/L (for solution composition, see the caption to Fig. 1).

diffusion of the metal from the amalgam begins to play a substantial role in the process, and equation (5) becomes inapplicable.

Figure 3 shows the dependence of the anodic-peak potentials on the film thickness. The slope of the straight lines in the plot \(\varphi_{\mathrm{p}}, \lg d - b/\beta = 0.09\) coincides (within the limits of experimental error) with the slope of the straight lines \(\varphi_{\mathrm{p}}, \lg W\), which is in agreement with equation (5).

Fig. 3. Dependence of the potentials of the peaks of the anodic waves of zinc on the thickness of the amalgam film at two concentrations of ammonia (ligand) in solution: 1—\(1.0\ \mathrm{mol/l}\); 2—\(0.13\ \mathrm{mol/l}\).

In the region of large values of \(d\), the peak potentials depend only very weakly on the film thickness, since the effect of diffusion of metal atoms from thick films is manifested (conditions of semi-infinite diffusion). At a very small film thickness (less than \(3\ \mu\)), the dependence also differs from the theoretical one. The deviation from the theoretical straight line is possibly connected with the fact that, because of the roughness of the surface of the silver wire, very thin films do not have the same thickness over the entire surface.

The distances between the straight lines in Figs. 1 and 3 correspond to \(q_2 = 1.2\) (according to [8], \(q_2 = 1\); in [7], \(q_2 = 0.6\)). Thus, the limiting equation for an irreversible anodic wave at a stationary mercury film electrode agrees satisfactorily with the experimental data at very low rates of potential change \((W < 1\ \mathrm{V/min})\) and small thicknesses of the mercury film of the electrode \((d < 10\ \mu)\).

Conclusions

1. Experiments have been carried out to study the influence, on the peak potential of the anodic wave of zinc, of the rate of potential change and of the thickness of the amalgam film at different concentrations of ammonia (ligand) in solution.

2. It has been shown that, when working under the conditions of the APA method with self-recording polarographs, the limiting equation of the anodic wave agrees satisfactorily with the experimental data at low rates of potential change and small thicknesses of the mercury film of the electrode.

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